Compressor Equation

Please give me the equation with a link if possible for determining power for a compressor. I know volume x pressure differential / efficiency but I think the gas being compressed also is a factor. Thank you.

Hello, I'm working on a model of a fan and I have the characteristic curves Flow/impelled power and flow/total pressure.

I also have the relation of adiabatic compression you have written but it concerns the Head (in meters) and not the mass flowrate. Therefore, my question is : how do you get the outlet pressure of a fan knowing the characteristic curves and the formula with the head ?

More clearly that possible to convert the Head (m) into a differential pressure (Pout-Pin) or even the outlet Pressure of the fan (Pout) ?